Sampling rate effects on measurements of correlated and biased random walks

When observing the two-dimensional movement of animals or microorganisms, it is usually necessary to impose a fixed sampling rate, so that observations are made at certain fixed intervals of time and the trajectory is split into a set of discrete steps. A sampling rate that is too small will result in information about the original path and correlation being lost. If random walk models are to be used to predict movement patterns or to estimate parameters to be used in continuum models, then it is essential to be able to quantify and understand the effect of the sampling rate imposed by the observer on real trajectories. We use a velocity jump process with a realistic reorientation model to simulate correlated and biased random walks and investigate the effect of sampling rate on the observed angular deviation, apparent speed and mean turning angle. We discuss a method of estimating the values of the reorientation parameters used in the original random walk from the rediscretized data that assumes a linear relation between sampling time step and the parameter values.     

Foray search: an effective systematic dispersal strategy in fragmented landscapes

In the absence of evidence to the contrary, population models generally assume that the dispersal trajectories of animals are random, but systematic dispersal could be more efficient at detecting new habitat and may therefore constitute a more realistic assumption. Here, we investigate, by means of simulations, the properties of a potentially widespread systematic dispersal strategy termed "foray search." Foray search was more efficient in detecting suitable habitat than was random dispersal in most landscapes and was less subject to energetic constraints. However, it also resulted in considerably shorter net dispersed distances and higher mortality per net dispersed distance than did random dispersal, and it would therefore be likely to lead to lower dispersal rates toward the margins of population networks. Consequently, the use of foray search by dispersers could crucially affect the extinction-colonization balance of metapopulations and the evolution of dispersal rates. We conclude that population models need to take the dispersal trajectories of individuals into account in order to make reliable predictions.     

The evolution of dispersal in random environment

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.     

Why the null matters: statistical tests,random walks and evolution

A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the scaled maximum, the log-rate-interval (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The runs test in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.     

Limited capacity of working memory in unihemispheric random walks implies conceivable slow dispersal

Phenomenologically inspired by dolphins’ unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker’s risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.     

How landscapes affect the evolution of dispersal behaviour in reef fishes: results from an individual‐based model

The vast majority of tropical reef fishes have a sedentary adult phase and pelagic larval phase that is potentially highly dispersive. Dispersal may be favoured by a wide range of factors including the arrangement of suitable habitat in space. In this paper the dispersal strategy of individuals is followed and allowed to evolve in a simplified model of three different landscapes: an enclosed sea, an open archipelago and a barrier reef. The three landscapes have very different characteristics, but all have similar spatial clumping of reef habitat. In all landscapes, as minimum time to settlement increases, evolved movement strategy also increases and longer settlement windows favour dispersal. In the archipelago movement is not maximized until the minimum pelagic duration is longer than in the other landscapes. The model predicts that, given the same pelagic duration, species from enclosed seas should have more dispersive behaviours than those from open archipelagos, because of the density of habitat and the aggregation of habitat in space affect the likelihood of larvae finding suitable habitat for settlement.     

Estimating species' absence, colonization and local extinction in patchy landscapes: an application of occupancy models with rodents

Making an inference on the absence of a species in a site is often problematic, due to detection probability being, in most cases, <1. Inference is more complicated if detection probability, together with distribution patterns, vary during the year, since the possibility of inferring a species absence, at reasonable costs, may be possible only in certain periods. Our aim here is to show how such challenging situations can be by tackled by applying some recently developed occupancy models combined with sample size (number of repeated surveys) estimation. We thus analysed the distribution of two rodents Myodes glareolus and Mus musculus domesticus in a fragmented landscape in central Italy pointing out how it is possible to identify true absences, non-detections, extinctions/colonizations and determine seasonal values of detection probability.     

Adaptive walks on behavioural landscapes and the evolution of optimal behaviour by natural selection

Summary One of the main challenges to the adaptationist programme in general and to the use of optimality models in behavioural and evolutionary ecology in particular is that natural selection need not optimise fitness. This challenge is addressed by considering the evolution of optimal patch choice by natural selection. The behavioural model is based on a state variable approach in which a strategy consists of a sequence denoting the patch to be visited as a function of the organism's state and time. The optimal strategy maximises expected terminal reproduction. The fitnesses of alternative strategies are computed by iteration of the associated equations for fitness; this characterises the adaptive behavioural landscape. There may be enormous numbers of strategies that have near optimal fitnesses. A population model is used to connect frequencies of behavioural types from one generation to the next. Theories on adaptive walks on fitness landscapes are considered in the context of behaviour. The main result is that within the context of optimality arguments at selective equilibrium, sub-optimal behaviours can persist. General implications for research in behavioural ecology, including tests of behavioural theories, are discussed.     

The evolution of dispersal

A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a spread parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected. S. Martinez was partially supported by Fondecyt 1020126 and Fondecyt Lineas Complementarias 8000010. K. Mischaikow was supported in part by NSF Grant DMS 0107396. Key words or phases:Non-local dispersal – Integral kernel – Evolution of dispersal     

Edge effects in patchy seagrass landscapes: The role of predation in determining fish distribution

Predation is often described as an underlying mechanism to explain edge effects. We assessed the importance of predation in determining edge effects in seagrass using two approaches: a video survey to sample predators at small scales across seagrass edges, and a tethering experiment to determine if predation was an underlying mechanism causing edge effects. Underwater videos were placed at four positions: middle of seagrass patches; edge of seagrass; sand immediately adjacent to seagrass and sand distant from seagrass. Fish abundances and the time fish spent in view were measured. The main predatory fish (Australian salmon, Arripis spp.) spent more time over adjacent sand than other positions, while potential prey species (King George whiting, Sillaginodes punctata (Cuvier), recruits) were more common in the middle of seagrass patches. Other species, including the smooth toadfish, Tetractenos glaber (Freminville), and King George whiting adults, spent more time over sand adjacent to seagrass than distant sand, which may be related to feeding opportunities. King George whiting recruits and pipefish (Stigmatopora spp.) were tethered at each of the four positions. More whiting recruits were preyed upon at outer than inner seagrass patches, and survival time was greater in the middle of shallow seagrass patches than other positions. Relatively few pipefish were preyed upon, but of those that were, survival time was lower over sand adjacent to seagrass than at the seagrass edge or middle. Video footage revealed that salmon were the dominant predators of both tethered King George whiting recruits and pipefish. The distribution of predators and associated rate of predation can explain edge effects for some species (King George whiting) but other mechanisms, or combinations of mechanisms, are determining edge effects for other species (pipefish).     

Woodland birds in patchy landscapes: the evidence base for strategic networks

Habitat creation and management within wooded networks is a potentially effective strategy to reduce ecological isolation and the deleterious effects of fragmentation. However, questions remain over the relative advantages of different approaches, e.g. buffering patches vs. increasing connectivity. Potential effects of woodland fragmentation include reduction in regional woodland cover, reduced patch size, edge effects with loss of core habitat, and increased isolation with disruption of dispersal and metapopulation dynamics. We adopt an evidence-based approach to review how each of these affects woodland birds with an emphasis on studies from the UK and use this to identify management priorities for mitigation. There is evidence for both patch area and composition effects: larger woodlands support more woodland bird species, and woods located within sparsely wooded landscapes are less valuable to specialist woodland species. Bird assemblages show a nested pattern with respect to area, and thus species found in small woods also occur in large woods but not vice versa. However, small woods may be preferred by a few edge species, while small woods also have greater variability in bird species composition. Consideration of the metapopulation dynamics of specialist species with poor dispersal shows that creating or buffering large woodlands is more efficient than a greater total area of small fragments. Connectivity appears most useful for widespread generalist species with almost continuous populations. Woodland structure and quality are of overwhelming importance: as well as mature woodland, young growth, scrub and edges are also key components. There is an urgent need to examine the relationship between nest predation and landscape structure within UK woodlands.     

The evolution of density-dependent dispersal

Despite a large body of empirical evidence suggesting that the dispersal rates of many species depend on population density, most metapopulation models assume a density-independent rate of dispersal. Similarly, studies investigating the evolution of dispersal have concentrated almost exclusively on density-independent rates of dispersal. We develop a model that allows density-dependent dispersal strategies to evolve. Our results demonstrate that a density-dependent dispersal strategy almost always evolves and that the form of the relationship depends on reproductive rate, type of competition, size of subpopulation equilibrium densities and cost of dispersal. We suggest that future metapopulation models should account for density-dependent dispersal     

Investigating the dispersal routes used by an invasive amphibian, Lithobates catesbeianus, in human-dominated landscapes

Clarifying how species move across and utilize human-modified landscapes is key to the conservation of declining populations, as well as to the management and control of invasive species. The North American bullfrog (Lithobates catesbeianus) is a globally distributed invasive amphibian that has been implicated in the decline of native amphibians across its invasive range and may also act as a transport vector for a number of deadly amphibian pathogens. Identifying the landscape-level features that facilitate or hinder this species as it moves across an ever-changing landscape is necessary to inform control efforts and limit this species’ impact on already declining amphibian populations. We conducted surveys of 243 wetlands across the Colorado Front Range and used an information-theoretic approach to evaluate the contribution of wetland-specific characteristics and landscape-level factors in determining the detection of bullfrog populations and breeding bullfrog populations. Specifically, our goal was to determine whether features related to overland dispersal or to the connectivity of wetlands were better predictors of bullfrog occurrence. Our results indicated that landscape-level factors that may either hinder or facilitate overland movement, such as topographic complexity and the density of wetlands, were the best predictors of bullfrog occurrence at the scale of our analysis, rather than characteristics relating to the connectivity of wetlands to lotic waterway systems. We suggest that when considering the control or eradication of this species, efforts should be directed at reducing hydroperiod of wetlands and should target regions with a high density of wetlands and/or low topographic relief.     

Evolutionary stability of ideal free dispersal strategies in patchy environments

A central question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionarily stable. Hastings (Theor Pop Biol 24:244-251, 1983) showed that among unconditional dispersal strategies in a spatially heterogeneous but temporally constant environment, the dispersal strategy with no movement is convergent stable. McPeek and Holt's (Am Nat 140:1010-1027, 1992) work suggested that among conditional dispersal strategies in a spatially heterogeneous but temporally constant environment, an ideal free dispersal strategy, which results in the ideal free distribution for a single species at equilibrium, is evolutionarily stable. We use continuous-time and discrete-space models to determine when the dispersal strategy with no movement is evolutionarily stable and when an ideal free dispersal strategy is evolutionarily stable, both in a spatially heterogeneous but temporally constant environment.     

Foraging strategy of cattle in patchy grassland

We tested several strategies of foraging that grazing herbivores may adopt in a patchy habitat in relation to energy intake. The patch selection of cattle was investigated in an Agrostis/Festuca grassland and in a Lolium grassland in 13 observation periods over 2 years. Both grasslands were stocked with five yearling steers. Bite counts were made on patches of different vegetation structure: short, tall and mature stemmy grass. Bite size of each patch category was determined by hand-plucking. Samples of patch types were analysed for organic matter digestibility, as a measure of energy content. There was a large seasonal variation in relative patch cover and in forage characteristics. However, the differences between patches in bite size, bite rate and digestibility were consistent over time. In short patches digestibility was high, bite size was low and bite rate was high compared to stemmy patches. In tall patches digestibility was only little lower than in short patches and bite size and bite rate were intermediate between short and stemmy patches. The steers selected the short and tall patches over the stemmy patches, despite a relatively low intake rate of digestible organic matter in the short patches. Four hypotheses on foraging strategy were examined to explain the allocation of time or bites between patches: random allocation according to bites, random allocation according to grazing time, matching of time in proportion to digestibility, and matching of time in proportion to intake rate of digestible organic matter. The observed distribution of bites and time between patches was significantly different from the predictions of the various hypotheses. Patch choice was better explained by a random allocation of grazing time than by a random allocation of bites. Matching for digestible organic matter intake rate yielded the worst predictions of patch selection. Matching for digestibility gave the best explanation of patch selection, but the improvement compared to a random allocation of grazing time was not significant. The significance of the contribution of digestibility to selection may have been confounded by the effect of increased selectivity within tall patches. Observed patch selection was considered in relation to the maximization of energy intake rate. The selectivity of cattle was not pronounced, but it was consistent with a principle of maximization of energy intake on a daily basis instead of a short-term basis. Selectivity appeared to be constrained by costs of searching for and discriminating between different forage resources. It is concluded that a flexible selection for short patches over tall patches and avoidance of stemmy patches provides a good approximation of energy intake maximization in a complex and changing environment.     

Evolution of reduced dispersal mortality and 'fat-tailed' dispersal kernels in autocorrelated landscapes

Models describing the evolution of dispersal strategies have mostly focused on the evolution of dispersal rates. Taking trees as a model for organisms with undirected, passive dispersal, we have developed an individual-based, spatially explicit simulation tool to investigate the evolution of the dispersal kernel, P(r), and its resulting cumulative seed-density distribution, D(r). Simulations were run on a variety of fractal landscapes differing in the fraction of suitable habitat and the spatial autocorrelation. Starting from a uniform D(r), evolution led to an increase in the fraction of seeds staying in the home cell, a reduction of the dispersal mortality (arrival in unsuitable habitat), and the evolution of 'fat-tailed' D(r) in autocorrelated landscapes and approximately uniform D(r) in random landscapes. The evolutionary process was characterized by long periods of stasis with a few bouts of rapid change in the dispersal rate.     

Preference in patchy landscapes: the influence of scale-specific intake rates and variance in reward

Understanding the responses of foragers to patchy distributionsof resources has formed a fundamental challenge in behavioralecology. Two currencies have been used to assess the patch preferencesof herbivores—intake rate maximization and risk sensitivity.We wished to understand if small mammalian foragers, collaredlemmings (Dichrostonyx groenlandicus), choose patches to maximizefood intake rate or to reduce risk of starvation in "variable"environments. Moreover, we examined the possibility that maximizingintake rate depends on the spatial scale of patchiness. We designedan experiment offering two alternative patches of food, varyingthe predictability of food rewards and the "potential intakerate" at different spatial scales. Collared lemmings did notconsistently select patches that maximized their intake rateat either scale studied. Instead, they chose patches offeringthe least variation in food reward over the course of the experiment.Collared lemmings used prior knowledge gained from previousforaging bouts to assess food variability. We interpret theseresults as evidence for risk-averse foraging strategies, whichare predicted for continuous foragers aiming to minimize riskof starvation.